A ceramic-matrix composite having a multilayered interfacial coating adapted to protect the reinforcing fibers from long-term oxidation, while allowing these to bridge the wake of advancing cracks in the matrix, is provided by selectively mismatching materials within adjacent layers of the interfacial coating, the materials having different coefficients of thermal expansion so that a low toughness interface region is created to promote crack deflection either within an interior layer of the mismatched interfacial coating or between adjacent layers of the mismatched interfacial coating.